A194066 Natural fractal sequence of A087483.

1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1

Offset

1,3

Comments

See A194029 for definitions of natural fractal sequence and natural interspersion.

Links

Table of n, a(n) for n=1..97.

Mathematica

z = 70;
c[k_] := 1 + Floor[(1/3) k^2];
c = Table[c[k], {k, 1, z}]  (* A087483 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 300}]   (* A194066 *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 14}, {k, 1, n}]] (* A194067 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194068 *)

Crossrefs

Cf. A194029, A194067, A087483.

Sequence in context: A122197 A030718 A227779 * A308916 A353171 A182628

Adjacent sequences: A194063 A194064 A194065 * A194067 A194068 A194069

Keyword

nonn

Author

Clark Kimberling, Aug 14 2011

Status

approved